Subject: [mg80295] Re: Extracting terms of a multivariate polynomial order by order

From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>

Date: Thu, 16 Aug 2007 07:26:02 -0400 (EDT)

Organization: Uni Leipzig

References: <fa13t2$p5c$1@smc.vnet.net>

Reply-to: kuska at informatik.uni-leipzig.de

Hi,
CoefficientArrays[Expand[(1 + x + y + z)^3], {x, y, z}] /.
s_SparseArray :> Normal[s]
may help you.
Regards
Jens
Marcus P S wrote:
> Hello,
>
> I have a multivariate polynomial (3 variables) from which I would
> like to extract terms order by order. More explicitly, I want all the
> lowest order terms, or all terms of the form
>
> c(L,M,N) x^L y^M z^N
>
> where L+M+N is smallest, and c(LMN) is some coefficient. If I have
> this, I can extract order by order, and taylor to which order I want
> to approximate my polynomial.
>
> I considered "Coefficients", but if I ask for the coefficients of
> the form x^2 z^2, it may return something like "1 + y", which is not
> what I want. Moreover, I have to explicitly request each possible
> term of a given order, which seems too mechanical/repetitive to be the
> "right way" to do things. The function for manipulating SeriesData
> objects are similarly limited.
>
> I am assuming that there is function in Mathematica (even 5.2) that
> will do this. Any suggestions would be greatly welcome.
>
> Thanks in advance.
>
> Marcus Silva
>
>